The head of the armed forces, Air Chief Marshal Sir Jock Stirrup, giving evidence to the Iraq inquiry today. Photograph: PA

British troops were sent to Iraq without sufficient body armour because the government's rush to war meant that the military "simply didn't have enough time" to source all the necessary equipment, the inquiry into the conflict heard today.

Air Chief Marshal Sir Jock Stirrup, the head of the armed forces, told the Chilcot inquiry that being allowed six months to prepare for a large deployment – instead of the four that defence chiefs were given – would have made a "significant difference" to the provision of kit such as body armour and desert combats.

"The problem of course was that we simply didn't have enough time, as it turned out, to do everything we needed to do before the operation started," he said.

Stirrup said the forces did not have enough enhanced combat body armour. "I think in part for both clothing and body armour, the issue was it was all done so rapidly at the last minute, no one was quite sure who had what.

"For example, just before the start of operations, the clear message that we were receiving in the Ministry of Defence was that all unit demands for enhanced combat body armour had been met. But quite clearly not everybody who needed it in theatre got it."

Asked whether having an extra two months to prepare for the war would have helped, he replied: "I think it would have made a significant difference. That's 50% additional time. We were finding that in a number of cases we were getting 100% delivery about a month or two after the operation started. So I think that the six-month assumption wasn't a bad one."

Stirrup said defence chiefs had warned the government of their concerns about the rushed pace of the deployment. "We made it absolutely clear to ministers that if we were not allowed to engage with industry – and that was the critical element – we could take these no further and that there was a serious risk that they would not all be delivered by the assumed start of operations," he said.

Stirrup, who was deputy chief of defence staff (equipment) at the time of the invasion, singled out problems with supplying enough body armour, desert combats and boots for frontline troops. He said the accelerated timetable had led to considerable confusion between the Ministry of Defence and soldiers in the field over how much body armour was needed.

The shortage of body armour was blamed for the death of one of the first British soldiers killed in Iraq. Tank commander Sergeant Steven Roberts, 33, who was born in Cornwall and lived in Shipley, West Yorkshire, was shot dead by a comrade while struggling with an attacking Iraqi near the southern city of Zubayr on March 24 2003. The 2006 inquest into his death heard he was left exposed by "serious failings" in the army's supply and training methods which meant he had to give up his body armour just three days earlier.

Stirrup told the inquiry that although the required equipment was sometimes delivered to the conflict zone, it did not always end up in the right place. "It's clear that lack of visibility on what was actually happening in theatre was hampering us," he said.

He also admitted that the government's decision to deploy extra troops to southern Afghanistan in January 2006 had made military chiefs "very nervous" about overstretching British forces.

"There was absolutely this concern about the overlap between Iraq and Afghanistan, and the doubt whether we would actually be able to reduce in Iraq quite as quickly as we were planning at that time," he said.

He went on: "We would have preferred to see some substantive drawdown movement in our deployment in Iraq before going into Afghanistan."

Stirrup said one of the key lessons of the Iraq war was that military intervention tended to involve lengthy commitment. "When you go in, you're going to be committed; you are quite likely to be committed for a long time and you are going to be stuck," he said.

"It's not the sort of environment where you can just pick up your ball halfway through the game and go home. You have got to see it through, and you have got to see it through to a successful conclusion."

Understanding the potential commitment when making a military intervention, he added, was "absolutely crucial".

He also told the inquiry that the shortage of helicopters available to British troops was "not a significant issue" in Iraq.

However, he was scathing about the botched deal that led to eight Chinook Mk3 helicopters standing idle for more than eight years because the MoD had failed to secure access to their software source code when it bought them.

When asked about former defence secretary John Hutton's claim last week that it would be hard to imagine a "worse procurement shambles" than the delayed Future Rapid Effect System programme to provide new armoured vehicles, he replied: "It's quite easy to imagine a worse one, and that's the Chinook Mk3."